which follows from (REF ) by using the fact that \(\sqrt{-g}\mathcal {L}_{m}\)  is a homogenous function of the inverse metric \(g^{\mu \nu }\)  of degree \(\left(m-\frac{D}{2}\right)\)  [1]}. Applying to cubic Lovelock gravity gives \((\mbox{for} \,\zeta =1, \sigma =1)\) ,
\(D\mathcal {L}_{m=0}+(D-2)\mathcal {L}_{m=1}+\alpha L^2 (D-4)\mathcal {L}_{m=2}+\beta L^4(D-6) \mathcal {L}_{m=3}=0,\) 
